In total our algorithm, that implements the optimization (REF ), is optimizing three objects \(\phi , \sigma _x\)  and \(\sigma _y\) . While \(\phi \)  and \(\sigma _y\)  can be optimized as in the corresponding non-EiV model, the optimization w.r.t \(\sigma _x\)  needs some discussion. Using (REF ) this optimization can be implemented via the reparametrization trick and is influenced by the chosen \(\lambda _\zeta \) . If we let \(\lambda _\zeta \rightarrow \infty \)  as described in Subsection REF  we found, for the examples from Section , that the optimization (REF ) often led to vanishing \(\sigma _x\) .At least when looking at the maximum likelihood solution of the EiV model (REF ) this behavior appears sensible as the likelihood becomes infinite for \(\sigma _x=0\)  and \(\zeta _i=x_i\)  if there are no "duplicate" \(x_i\)  with different labels in the data. To prevent this from happening, we here propose, at least for large or infinite \(\lambda _\zeta \)  to use the Deming regression [1]}, that is
\(\sigma _x = \delta \cdot \sigma _y \,.\) 
